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So, what do you think? Personally, I think we'd still be the same person. I mean, it's not a physical body that makes us who we are. Idk :shrug:
It's difficult to say.
If you take your memories and put them into something else, is it you? It's a re-hash of the Star Trek Teleporter Conundrum... "So, this thing tears me apart and puts me back together... is what comes out the other side really me, or do I die when I enter this thing and something else continues to act like me?"
What we do know, however, is that personality is a complex thing, and no single 'component' is responsible for it, but many influence it. For example - much of human language is related to the human experience. "This plan stinks." "He showed his true colors." "They will bend over backwards for you." These are all portions of our speech that speak to the human experience - it's difficult and compromising to bend over backwards - hence why we use the expression across many different languages and cultures. If you were a computer - this would have no meaning (though if a computer system were built from a in-depth scan of your brain, it may be able to properly understand the question - though long-term separation from a peripheral nervous system and 'the human experience' would likely begin to convert the personality into something other than human).
Think about how often these concepts are used... "I can't put my finger on it." "It's on the tip of my tongue." - we intentionally develop emoticons and other such things to give our conversations a more 'personable' feel to them.
Personality is more than memory, more than 'wetware' - but each of those things influence it. 'Hard' answers to the question may never be possible and always remain philosophical.